Shadow Magnetic Hamiltonian Monte Carlo

Quantum-inspired magnetic Hamiltonian Monte Carlo

“…This results in faster convergence to the correct target density, and much lower auto-correlations between the generated samples when compared to HMC [4,6,26]. When the magnetic component of MHMC is absent, MHMC and HMC have the same dynamics [4,6,26]. MHMC has similar execution times to HMC, which illustrates the close relationship between HMC and MHMC.…”

“…The inference of complex probabilistic models using Markov Chain Monte Carlo (MCMC) algorithms has become very common [1][2][3][4][5][6][7]. MCMC methods have been successfully applied in a variety of fields including health, finance and cosmology [1,4,5,[8][9][10][11][12][13][14][15].…”

“…HMC introduces the mass matrix for the momentum variable, trajectory length and step size parameters that need to be tuned for optimal results. Extensions of HMC include Riemannian Manifold Hamiltonian Monte Carlo (RMHMC) [1], the No-U-Turn Sampler (NUTS) [22] and Magnetic Hamiltonian Monte Carlo (MHMC) [6]. Furthermore, machine learning techniques have also been utilised to enhance the efficiency of Monte Carlo sampling algorithms.…”

“…This removes the need for manual tuning of these parameters and the associated costly pilot runs, making HMC more accessible to non-experts. A recent extension to HMC is MHMC which adds a magnetic field to HMC [6]. This results in faster convergence to the correct target density, and much lower auto-correlations between the generated samples when compared to HMC [4,6,26].…”

“…A recent extension to HMC is MHMC which adds a magnetic field to HMC [6]. This results in faster convergence to the correct target density, and much lower auto-correlations between the generated samples when compared to HMC [4,6,26]. When the magnetic component of MHMC is absent, MHMC and HMC have the same dynamics [4,6,26].…”